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The family
${\mathcal{F}}_{\unicode[STIX]{x1D706}}$
of orientation-preserving harmonic functions
$f=h+\overline{g}$
in the unit disc
$\mathbb{D}$
(normalised in the standard way) satisfying
for some
$$\begin{eqnarray}h^{\prime }(z)+g^{\prime }(z)=\frac{1}{(1+\unicode[STIX]{x1D706}z)(1+\overline{\unicode[STIX]{x1D706}}z)},\quad z\in \mathbb{D},\end{eqnarray}$$
$\unicode[STIX]{x1D706}\in \unicode[STIX]{x2202}\mathbb{D}$
, along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in
${\mathcal{F}}_{\unicode[STIX]{x1D706}}$
are convex.
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